Answer
407.1k+ views
Hint: We know that the sum of all angles of a triangle is $180^\circ $. An isosceles triangle consists of two base angles and one vertex angle. We can say that the measure of two base angles will be the same. Add the vertex angle and base angles equate them to $180^\circ $, find the measure of base angle.
Complete step-by-step answer:
We know that an isosceles triangle consists of a vertex angle and two base angles. Length of two sides of the isosceles triangle is equal. So, the measure of two base angles of the isosceles triangle is equal.
Let us consider the measure of base angle to be $x$ degree. So, the measure of two angles are $x$ and $x$. The measure of vertex angle is $84^\circ $.
We know that the sum of all angles of a triangle is $180^\circ $. We can calculate the measure of base angle as:
\[x + x + 84^\circ = 180^\circ \]
\[ \Rightarrow 2x + 84^\circ = 180^\circ \]
Subtract $84^\circ $ from both the sides of the above equation, we get
\[ \Rightarrow 2x = 96^\circ \]
Divide both the sides by 2 to find the measure of base angle.
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{96^\circ }}{2}\]
\[ \Rightarrow x = 48^\circ \]
Therefore, the measure of the base angle of the isosceles triangle is $48^\circ $.
So, option (D) is the correct answer.
Note: We need to recognise that the measure of two base angles of an isosceles triangle is equal to each other as they are formed by two equal sides. Carefully consider that the missing two angles are base angles. So, consider the other two angles as $x$.
If we consider two equal angles of an isosceles triangle as $84^\circ $, then it may lead to incorrect answers.
Complete step-by-step answer:
We know that an isosceles triangle consists of a vertex angle and two base angles. Length of two sides of the isosceles triangle is equal. So, the measure of two base angles of the isosceles triangle is equal.
Let us consider the measure of base angle to be $x$ degree. So, the measure of two angles are $x$ and $x$. The measure of vertex angle is $84^\circ $.
![seo images](https://www.vedantu.com/question-sets/8b575538-9d2c-4162-8a3f-0b1e544988a32403811540891894317.png)
We know that the sum of all angles of a triangle is $180^\circ $. We can calculate the measure of base angle as:
\[x + x + 84^\circ = 180^\circ \]
\[ \Rightarrow 2x + 84^\circ = 180^\circ \]
Subtract $84^\circ $ from both the sides of the above equation, we get
\[ \Rightarrow 2x = 96^\circ \]
Divide both the sides by 2 to find the measure of base angle.
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{96^\circ }}{2}\]
\[ \Rightarrow x = 48^\circ \]
Therefore, the measure of the base angle of the isosceles triangle is $48^\circ $.
So, option (D) is the correct answer.
Note: We need to recognise that the measure of two base angles of an isosceles triangle is equal to each other as they are formed by two equal sides. Carefully consider that the missing two angles are base angles. So, consider the other two angles as $x$.
If we consider two equal angles of an isosceles triangle as $84^\circ $, then it may lead to incorrect answers.
Recently Updated Pages
What are the figures of speech in the poem Wind class 11 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Two tankers contain 850 litres and 680 litres of petrol class 10 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when eggshell is added to nitric acid class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why was Kamaraj called as Kingmaker class 10 social studies CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What makes elections in India democratic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
One cusec is equal to how many liters class 8 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What organs are located on the left side of your body class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)